Answer: 81/100
Step-by-step explanation:
I don't guarantee you I am right but..
first, solve for the exponents after substituting the numbers in
3/5 x 3/5 is 9/25
since b's exponent is negative, you change the fraction into its reciprocal and then do it with the exponent but positive
2/3^-3 to 3/2^3 and 3/2 x 3/2 is 9/4
then you mutiply both numbers to get 9/4 x 9/25 is 81/100
Answer: To know whether a radical expression is in simplest form or not you should put the numbers and letters inside the radical in terms of prime factors. Then, the radical expression is in the simplest form if all the numbers and letters inside the radical are prime factors with a power less than the index of the radical
Explanation:
Any prime factor raised to a power greater than the index of the root can be simplified and any factor raised to a power less than the index of the root cannot be simplified
For example simplify the following radical in its simplest form:
![\sqrt[5]{3645 a^8b^7c^3}](https://tex.z-dn.net/?f=%20%5Csqrt%5B5%5D%7B3645%20a%5E8b%5E7c%5E3%7D%20)
1) Factor 3645 in its prime factors: 3645 = 3^6 * 5
2) Since the powr of 3 is 6, and 6 can be divided by the index of the root, 5, you can simplify in this way:
- 6 ÷ 5 = 1 with reminder 1, so 3^1 leaves the radical and 3^1 stays in the radical
3) since the factor 5 has power 1 it can not leave the radical
4) the power of a is 8, then:
8 ÷ 5 = 1 with reminder 3 => a^1 leaves the radical and a^3 stays inside the radical.
5) the power of b is 7, then:
7 ÷ 5 = 1 with reminder 2 => b^1 leaves the radical and b^2 stays inside the radical
6) the power of c is 3. Since 3 is less than 5 (the index of the radical) c^3 stays inside the radical.
7) the expression simplified to its simplest form is
![3ab \sqrt[5]{3.5.a^3b^2c^3}](https://tex.z-dn.net/?f=3ab%20%5Csqrt%5B5%5D%7B3.5.a%5E3b%5E2c%5E3%7D%20)
And you know
it cannot be further simplified because all the numbers and letters inside the radical are prime factors with a power less than the index of the radical.
Answer:
B
Step-by-step explanation:
9514 1404 393
Answer:
22/44
Step-by-step explanation:
The probability of black is the ratio of black cards to all cards. If the Ace and 2 are removed from each suit, there will be 11 of the 13 cards remaining. 2 suits are black, for a total of 2×11 = 22 black cards. Of course there are 4 suits altogether, for a total of 4×11 = 44 total cards. Then you have ...
P(black) = (black cards)/(total cards)
P(black) = 22/44
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You are expected to be familiar with the fact that a deck of 52 playing cards consists of 4 suits: diamonds, clubs, hearts, spades. Each suit has 13 cards, identified as Ace, 2, 3, ..., 10, Jack, Queen, King. The clubs and spades are black; the diamonds and hearts are red.